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Multiplication of a Binomial by a Monomial

If a=b2x,b=c2...

Question

If $a = b^{2 x}, b = c^{2 y}$ and $c = a^{2 z}$ , show that $8 x y z = 1$ .

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Solution

$a = b^{2 x}$ and $b = c^{2 y} \Rightarrow a = (c^{2 y})^{2 x} = c^{4 x y}$
Similarly, $a = c^{4 x y}$ and $c = a^{2 z} \Rightarrow a = (a^{2 z})^{4 x y} = a^{8 x y z}$
Now, $a = a^{8 x y z} \Rightarrow 8 x y z = 1$

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